2007 AMC 10A Problems/Problem 9
Contents
Problem
Real numbers and satisfy the equations and . What is ?
Solution 1
And
Substitution gives , and solving for yields . Thus .
Solution 2
Simplify equation which is , to , which equals .
And
Simplify equation which is , to , which equals .
Now, eliminate the bases from the simplified equations and to arrive at and . Rewrite equation so that it is in terms of . That would be .
Since both equations are equal to , and and are the same number for both problems, set the equations equal to each other.
Now plug , which is back into one of the two earlier equations.
Therefore the correct answer is E
See also
2007 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 8 |
Followed by Problem 10 | |
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All AMC 10 Problems and Solutions |
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